Theorems · Theorem · real analysis
ContDiffAt.continuousAt
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
{x : E} {n : WithTop ℕ∞}, ContDiffAt 𝕜 n f x → ContinuousAt f x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- ContinuousAtstatement · cited by 697
- ContDiffAtstatement and proof · cited by 262
- ContDiffWithinAt.continuousWithinAtproof · cited by 11
Cited by9
Results whose statement or proof uses this declaration.
- Real.contDiffAt_logproof · cited by 3
- ContDiffAt.continuousAt_iteratedFDerivproof · cited by 3
- OpenPartialHomeomorph.contDiffAt_symmproof · cited by 3
- InnerProductSpace.HarmonicOnNhd.continuousOnproof · cited by 2
- Complex.contDiffAt_tanproof · cited by 1
- Real.contDiffAt_tanproof · cited by 1
- ContDiffPointwiseHolderAt.continuousAtproof · cited by 1
- ContDiffAt.continuousAt_fderivproof · cited by 0
- map_add_eq_sum_add_integral_iteratedFDerivproof · cited by 0